Question

Find the area of the triangle whose vertices are (5,1), (3,5), (5,2)
(a) 1 sq. units (b) 28 sq. units (c) 24 sq. units (d) None of these

Answer 1

Answer:

The correct option is :

(a) 1 sq. units

Step-by-step explanation:

Let us consider the vertices of the triangle be A , B and C

Thus , A( 5 , 1) , B(3 , 5) and C(5 , 2)

Formula to be used

$area \: of \: triangle = | \frac{1}{2} [x_{1}(y_{2} - y_{3} ) + x_{2}( y_{3} - y_{1}) + x_{3}( y_{1} - y_{2} )]|$

Now using the formula we get ,

$ar.(ABC) = |\frac{1}{2} \times [5(5 - 2) + 3(2 - 1) + 5(1 - 5)] | \\ \implies ar.(ABC) = | \frac{1}{2} \times [5 \times 3 + 3 \times 1 + 5 \times ( - 4)] | \\ \implies ar.(ABC) = | \frac{1}{2} \times (15 + 3 - 20) | \\ \implies ar.(ABC) = |\frac{1}{2} \times ( - 2) | \\ \implies ar.(ABC) = | - 1| \\ \implies ar.(ABC) = 1sq. \: units$